Set-Membership Filtering-Based Leader-Follower Synchronization of Discrete-time Linear Multi-Agent Systems

TL;DR

This paper introduces a set-membership filtering approach for leader-follower synchronization in discrete-time linear multi-agent systems with unknown initial states and bounded disturbances, ensuring bounded disagreement errors.

Contribution

It proposes a novel set-membership filter-based control protocol that handles uncertainties and achieves synchronization with bounded errors in multi-agent systems.

Findings

The proposed filter effectively estimates agent states under disturbances.

Synchronization errors are proven to be bounded and decrease monotonically.

Simulations demonstrate the protocol's effectiveness in practical scenarios.

Abstract

In this paper, a set-membership filtering-based leader-follower synchronization protocol for discrete-time linear multi-agent systems is proposed wherein the aim is to make the agents synchronize with a leader. The agents, governed by identical high-order discrete-time linear dynamics, are subject to unknown-but-bounded input disturbances. In terms of its own state information, each agent only has access to measured outputs that are corrupted with unknown-but-bounded output disturbances. Also, the initial states of the agents are unknown. To deal with all these unknowns (or uncertainties), a set-membership filter (or state estimator), having the `correction-prediction' form of a standard Kalman filter, is formulated. We consider each agent to be equipped with this filter that estimates the state of the agent and consider the agents to be able to share the state estimate information with the neighbors locally. The corrected state estimates of the agents are utilized in the local control law design for synchronization. Under appropriate conditions, the global disagreement error between the agents and the leader is shown to be bounded. An upper bound on the norm of the global disagreement error is calculated and shown to be monotonically decreasing. Finally, two simulation examples are included to illustrate the effectiveness of the proposed set-membership filter and the proposed leader-follower synchronization protocol.